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Lawrence Berkeley National Laboratory Recent

Title Ultraefficient power conversion by band-edge spectral filtering.

Permalink https://escholarship.org/uc/item/2kh465km

Journal Proceedings of the National Academy of of the of America, 116(31)

ISSN 0027-8424

Authors Omair, Zunaid Scranton, Gregg Pazos-Outón, Luis M et al.

Publication Date 2019-07-16

DOI 10.1073/pnas.1903001116

Peer reviewed

eScholarship.org Powered by the Digital Library University of California Ultraefficient thermophotovoltaic power conversion by band-edge spectral filtering

Zunaid Omaira,b,1, Gregg Scrantona,b,1, Luis M. Pazos-Outóna,2, T. Patrick Xiaoa,b, Myles A. Steinerc, Vidya Ganapatid, Per F. Petersone, John Holzrichterf, Harry Atwaterg, and Eli Yablonovitcha,b,2 aDepartment of Electrical Engineering and Computer , University of California, Berkeley, CA 94720; bMaterial Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720; cNational Renewable Laboratory, Golden, CO 80401; dDepartment of Engineering, Swarthmore College, Swarthmore, PA 19081; eDepartment of Nuclear Engineering, University of California, Berkeley, CA 94720; fPhysical Insights Associates, Berkeley, CA 94705; and gApplied , California Institute of , Pasadena, CA 91125

Contributed by , June 10, 2019 (sent for review February 27, 2019; reviewed by James Harris and Richard R. King) Thermophotovoltaic power conversion utilizes Here, we present experimental results on a thermophotovoltaic from a local source to generate in a photovoltaic cell. cell with 29.1 ± 0.4% power conversion efficiency at an emitter It was shown in recent years that the addition of a highly reflective temperatureof1,207°C.Thisisarecordforthermophotovoltaic rear mirror to a maximizes the extraction of . efficiency. Our cells have an average reflectivity of 94.6% for below- This, in turn, boosts the , enabling the creation of record- bandgap , which is the key toward subbandgap breaking solar efficiency. Now we report that the rear mirror can be photons. We predict that further improvements in reflectivity, used to create thermophotovoltaic systems with unprecedented high series resistance, material quality, and the radiation chamber thermophotovoltaic efficiency. This mirror reflects low-energy in- geometry will push system efficiency to >50%. Such a highly frared photons back into the heat source, recovering their energy. efficient thermophotovoltaic system can have significant impact Therefore, the rear mirror serves a dual function; boosting the as a power source for hybrid cars (32), unmanned (33), voltage and reusing thermal photons. This allows the deep-space probes (34–36), and (37, 38), as well possibility of a practical >50% efficient thermophotovoltaic system. as enabling efficient systems (39–41) for heat and Based on this reflective rear mirror concept, we report a thermopho- electricity. tovoltaic efficiency of 29.1 ± 0.4% at an emitter of 1,207 °C. The Regenerative Thermophotovoltaic System In an ideal thermophotovoltaic system employing reuse (Fig. energy | | | TPV | solar 2A), a hot emitter is surrounded by photovoltaic cells lining the walls of the chamber, collecting from the emitter. For efficient hotovoltaic devices generate electricity from thermal radia- recovery of unused photons, the photovoltaic cells are backed by Ption (1–6). In thermophotovoltaic energy conversion, first highly reflective rear mirrors. Such mirrors are needed, in any described (7) in 1956, photovoltaic cells convert thermal radia- case, to provide the voltage boost associated with luminescence tion from a local heat source to electricity. The key is to find a extraction. As shown in Fig. 2B, the below-bandgap recycled way to exploit the great majority of low-energy thermal photons component of the radiated spectrum rethermalizes within the that would otherwise be unusable in a . heat source after being reflected from the photovoltaic cell. Most effort in this regard has been directed toward engineering the hot emitter, making it spectrally selective such that it suppresses Significance the emission of low-energy photons (8, 9). In this arrangement, the spectral emissivity of the thermal source is tailored to the absorp- Thermophotovoltaic conversion utilizes thermal radiation to gen- tion edge of the photovoltaic cell (10, 11), as illustrated in Fig. 1A. erate electricity in a photovoltaic cell. On a solar cell, the addition The spectral filter has been implemented by photonic crystals (12– of a highly reflective rear mirror maximizes the extraction of lu- 17), (18–22), and rare- oxides (23, 24). minescence, which in turn boosts the voltage. This has enabled the We present a different approach. All new record-breaking solar creation of record-breaking solar cells. The rear mirror also reflects cells now include a rear mirror to assist in the extraction (25) of low-energy photons back into the emitter, recovering the energy. band-edge luminescence from the photovoltaic cell. For high-quality This radically improves thermophotovoltaic efficiency. Therefore, photovoltaic materials, the rate of internal photon generation is the luminescence extraction rear mirror serves a dual function; high. However, in devices with poor photon management, this is boosting the voltage, and reusing the low-energy thermal pho- typically wasted by a poorly reflecting at the rear of the tons. Owing to the dual functionality of the rear mirror, we device. When a highly reflective mirror is inserted, a bright internal achieve a thermophotovoltaic efficiency of 29.1% at 1,207 °C, a photon gas develops, maximizing the observed external lumines- temperature compatible with furnaces, and a new world record at cence flux associated with a large carrier concentration. This pro- below 2,000 °C. vides a voltage boost of ∼0.1 V at open circuit (26). Indeed, the Author contributions: Z.O., G.S., L.M.P.-O., M.A.S., V.G., P.F.P., J.H., H.A., and E.Y. de- development of a highly reflective rear mirror has been the main signed research; Z.O., G.S., L.M.P.-O., M.A.S., J.H., and E.Y. performed research; Z.O., driver of recent efficiency records in solar photovoltaics (27–29). L.M.P.-O., and E.Y. analyzed data; and Z.O., L.M.P.-O., T.P.X., and E.Y. wrote the paper. Serendipitously, such a rear mirror could also reflect below- Reviewers: J.H., Stanford University; and R.R.K., Arizona State University. B bandgap photons (Fig. 1 ). Unprecedented thermophotovoltaic The authors declare no conflict of interest. efficiency can be achieved by reflecting low-energy photons back This open access article is distributed under Creative Commons Attribution-NonCommercial- to reheat the blackbody emitter, while utilizing the high-energy NoDerivatives License 4.0 (CC BY-NC-ND). photons for photovoltaic . In effect, the 1Z.O. and G.S. contributed equally to this work. band edge itself provides spectral selectivity, 2To whom correspondence may be addressed. Email: [email protected] or eliy@ without the need for a spectrally selective thermal emitter. This eecs.berkeley.edu. idea, first patented in 1967 (30), relies on the reuse of low-energy This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. photons (31), thus wasting no energy. We will call this process 1073/pnas.1903001116/-/DCSupplemental. “regenerative thermophotovoltaics.” Published online July 16, 2019.

15356–15361 | PNAS | July 30, 2019 | vol. 116 | no. 31 www.pnas.org/cgi/doi/10.1073/pnas.1903001116 AB Alternately, P P η = electrical = electrical , [1b] Pabsorbed Pelectrical + Qwaste

which is the conventional definition of heat engine efficiency, where Qwaste is the waste heat. Eqs. 1a and 1b assume that the internal surfaces of the radi- ation chamber are completely covered by photovoltaic cells as shown in Fig. 2. To the extent that the internal walls are not fully covered by photovoltaic cells, the remaining area of bare walls needs excellent reflectivity to produce a good net “effective Fig. 1. Increasing the efficiency of thermophotovoltaics by managing the reflectivity” that controls the system efficiency. low-energy thermal photons that cannot be absorbed by the semiconductor. The incident power Pincident(Ts) at an emitter temperature Ts There are two approaches for doing this. (A) Use a spectrally selective can be defined as the incident radiation flux bs(E, Ts) coating that will ideally emit high-energy photons or (B) exploit the semi- corrected by the spectral emissivity «(E) of the emitter [∼0.91 for conductor band edge itself as the spectral filter. The presence of a rear mirror ensures that any unabsorbed photons are reflected back to the graphite (44)], integrated over energy and area, emitter and are rethermalized. Z∞

PincidentðTsÞ = «ðEÞ bsðE, TsÞ · E dEA, [2] Photon reuse in this chamber—enabled by high mirror 0 reflectivity—results in high system efficiency. The system power conversion efficiency, η, is defined (42, 43) as the electrical where E is the photon energy and A is the surface area of the power generated by the photovoltaic cell, divided by the total photovoltaic cell. The cell absorptivity spectrum a(E), used to P thermal radiative power absorbed, determine absorbed, which is the denominator in the efficiency expressions (Eqs. 1a and 1b), can be directly known by measuring SCIENCES P P the cell reflectivity R(E), since a(E) = 1 − R(E). η = electrical = electrical [1a] APPLIED PHYSICAL P − P P , We can estimate the realistic thermophotovoltaic efficiency incident reflected absorbed based on the quality of the existing III-V materials that con- tributed to the current record-holding solar cells. The projected where Pincident is the incident power on the photovoltaic cell, and P is the power reflected from the cell. Eq. 1a is analogous thermophotovoltaic efficiency is shown in Fig. 3, which repre- reflected − to the efficiency definition of a solar cell, except that it accounts sents a realistic efficiency projection rather than ideal Shockley for the fact that reflected radiation is not lost but is rethermal- Queisser (45) performance. The optimum bandgap increases ized at the thermal source. Preflected is taken from the mea- slightly upon improving the rear reflectivity, to minimize ther- sured reflectivity spectrum of the photovoltaic cell, while malization losses from photons at the high-energy tail of the emitter Pincident is obtained from an accurate calibration of emitter spectrum. With an optimal bandgap, thermophotovoltaic temperature. efficiency can reach as high as >50%. For these calculations, we

A B 104 5.0

/eV) o 2 T =1200 C 4.0 blackbody PV cell 3.0 hν Eg Thermal emitter Recycled 2.0 power Eg=0.75 eV hν Eg PV cell Rear reflector 1.0

Spectral power density (W/cm 0 Mirror loss PV loss 0 0.2 0.4 0.6 0.8 1.0 1.2 Photon energy (eV)

Fig. 2. An ideal regenerative thermophotovoltaic system formed by a thermal radiation chamber, and power conversion inside the chamber. (A) High- energy (blue) photons from the emitter are converted to carriers in the photovoltaic cell, while low-energy (red) photons are reflected back to the emitter and rethermalized. (B) A highly reflective rear mirror is essential since a photon will need to be reflected many times before emerging in the high-energy tail of the Planck spectrum, for absorption in the semiconductor. Other losses in the photovoltaic cell arise due to poor material quality, as well as thermalization of high-energy carriers.

Omair et al. PNAS | July 30, 2019 | vol. 116 | no. 31 | 15357 parameterized the material quality by the internal luminescence power conversion efficiency η = Pelectrical=ðPincident − PreflectedÞ = η — efficiency int probability that carriers undergo radiative re- Pelectrical=Pabsorbed of a thermophotovoltaic device requires mea- — η = combination with a value int 98%. Such luminescence effi- surement of the total generated power (Pelectrical), the incident ciency has been reported for GaAs (46). power Pincident, and the reflected thermal power (Preflected)by Since the simple addition of a rear reflector can offer such high the device. efficiencies, it is tempting to consider the possibility of combining In an absolute calibration, the numerator is the electrical the rear reflector photovoltaic cells, with a spectrally tuned emitter. power, which is straightforward to measure. However, the power r ≡ −e For a spectrally tuned emitter with subbandgap reflectivity ( 1 ), absorbed is difficult to know, since it depends on multiple pa- R and a photovoltaic cell reflectivity , the total loss due to parasitic rameters. We now indicate how to measure the incident photon absorption is dependent on both of these reflectivities, as obtained flux and the fraction of it that is absorbed. through geometric progression of multiple reflections between the To measure the incident photon flux, we need to know 1) the emitter and the photovoltaic cell, emissivity of the emitter, 2) the geometrical view factor Feff; the ð − rÞð − RÞ fractional angle subtended by the emitter as viewed from a = 1 1 [3] parasitic . the photovoltaic cell as well as the multiple reflections between 1 − rR the photovoltaic cell, emitter, and the baffle used in our cham-

We can lower parasitic absorption aparasitic fraction by reflecting ber; and 3) the temperature of the emitter. low-energy photons using rear mirror (R ≈ 1), and by suppressing We establish methods to measure each of these parameters. emission of low-energy photons with spectral control of emitter 1) The emissivity « of graphite was measured experimentally radiation (r ≈ 1). (details in SI Appendix), obtaining a value of « ≈ 0.91, similar With R ≈ 1, the denominator of Eq. 3 becomes 1 − r, to other literature reports (44). leaving the total parasitic absorptivity dependent on the r ≈ 2) The geometrical view factor determines the short-circuit cur- quality of the rear mirror. On the other hand, if 1, implying rent from a black body. We calibrate the emitter temperature excellent spectral emissivity control, then the total parasitic ab- at 1,085 °C by slowly increasing the supplied electrical power a ≈ − r sorptivity parasitic 1 . Hence, in the presence of excellent until a copper bead that was previously placed on top of the emissivity control, the performance is almost entirely dominated emitter reaches its solid-to-liquid transition. Thus, by mea- by the high thermal emitter spectral reflectivity r. Whichever of R suring the short-circuit current at exactly 1,085 °C, we obtain or r is more ideal, is closer to unity, will dominate, and further the geometrical view factor. The relationship between the improvements in the other, nondominant reflectivity, r or R will short-circuit current, view factor, using Eq. 4, and Planck not contribute significantly. Therefore, it is sufficient to simply aim spectrum can be expressed: for the best rear reflectivity R, and to dispense with spectral emissivity control. Z∞ I ðT Þ = qAF « ðEÞ EQE ðEÞ b ðE T ÞdE [4] Efficiency Calibration SC s eff eff s , s . The purpose of this section is to validate the experimentally mea- 0 sured regenerative thermophotovoltaic efficiency. Under the re- generative principle, the reflected photon flux from the photovoltaic For calibration of Feff, we use the black body Planck spectrum cell reheats the thermal emitter and does not count against the bs(E, Ts) at a calibrated emitter temperature Ts = 1,085 °C, measured efficiency. Hence, the measurement (42, 43) of the EQE(E) is the measured external , and «eff(E) is the effective emissivity spectrum. (For our calcula- tions, we use an effective emissivity «eff instead of using the o emissivity « of graphite to take into account multiple reflec- Temitter= 1200 C 70 tions between the cell and the emitter. The effective emis- sivity, «eff is given by «/[1 − R(E)(1 − «)], where the 60 reflectivity spectrum, R(E), changes sharply when transition- ing to above the bandgap. The emissivity difference « – « e = 50 is ( eff )/ 5%, which to a shift of thermophoto- voltaic efficiency from 29.7 to 29.1%.) From this, we extract a F = 40 view factor eff 0.31. 3) Since the above procedure calibrates the geometrical view factor, which is temperature-independent, we can then 30 solve Eq. 4 to find the emitter temperature when Ts ≠ 1,085 °C. 20 Now, since we know the effective emissivity, geometrical view factor, and emitter temperature, we can accurately measure the 10 R∞ TPV conversion efficiency (%) efficiency conversion TPV incident flux, PincidentðTsÞ = AFeff «eff ðEÞbsðE, TsÞ · EdE. 0 0 90 91 92 93 94 95 96 97 98 99 We need to convert the incident spectrum to absorbed spec- Mirror reflectivity (%) trum, since any unabsorbed portion of the incident spectrum will be reflected back to the thermal emitter. For this, we measure Fig. 3. Projected thermophotovoltaic (TPV) system conversion efficiency the device’s absorptivity spectrum as (1 − reflectivity), which also versus effective mirror reflectivity. As reflectivity rises, the optimum bandgap rises. In absence of a rear mirror, only 8.5% efficiency is possible. includes the parasitic free carrier absorption of low-energy For this calculation, internal luminescence efficiency was assumed to be photons. The total absorbed power in the photovoltaic device 98%, along with zero series resistance and unity emissivity. is then

15358 | www.pnas.org/cgi/doi/10.1073/pnas.1903001116 Omair et al. P ðTsÞ = P − P absorbed incident reflected Au Au 2 μm Z∞ _ _ = AF « ðEÞð1 − RðEÞÞ bsðE, TsÞ · EdE. [5] + 18 -3 eff eff n -In0.55Ga0.45As (10 cm ) 200 nm 0 n+-InP (1018 cm-3) 20 nm With 1) emissivity calibration, 2) view factor calibration, and 3) temperature calibration, we can now accurately characterize the 17 -3 n-In0.55Ga0.45As (10 cm , 0.75eV) 2.5 μm device thermophotovoltaic efficiency. + 18 -3 100 nm Experiment p -InP (10 cm ) + 18 -3 The experimental chamber used for thermophotovoltaic mea- p -In0.69Ga0.31As0.67P0.33 (10 cm ) 200 nm surements is shown in Fig. 4. The thermal emitter is a graphite ribbon. Current is injected into the ribbon through its short ends + Rear reflector (Au) + to raise the temperature by heating. Beneath the ribbon, the photovoltaic cell is placed on a copper mount using thermally Handle (Si) conductive epoxy. For our experiment, we use an In0.55Ga0.45As photovoltaic cell with a bandgap of 0.75 eV, as shown in Fig. 5. Fig. 5. The cross-section of the photovoltaic cell is shown here. The InGaAs The total radiant power absorbed at different emitter tempera- active layer has a bandgap of 0.75 eV. The rear Au layer acts as the reflective tures and the corresponding generated are given in mirror. are collected by the front electrode grid, while holes are Fig. 6A. The thermophotovoltaic conversion efficiency, the ratio collected by the rear Au layer. between the electric power and the absorbed radiant power, is showninFig.6B, reaching a maximum of 29.1%, at 1,207 °C. At 2 emitter temperature is a trade-off between reducing the parasitic this temperature, we obtain Jsc, Voc, and fill factor of 918 mA/cm , 529 mV, and 0.73, respectively. Thisisforaphotovoltaiccellwith absorption of low-energy photons and the thermalization loss of an active area of 10 mm2, and corresponding external luminescence high-energy photons. We reduce the absorption of low-energy photons by using a highly reflective mirror. Then we use an SCIENCES efficiency of 3.5%, and with a corresponding internal luminescence = ∼ InGaAs active layer with bandgap 0.75 eV, well matched to an APPLIED PHYSICAL efficiency of 82%. The detailed procedure for extracting the lu- ∼ minescence efficiencies is given in SI Appendix. We limit our emitter temperature of 1,207 °C for reducing the thermaliza- emitter temperature to 1,200 °C, even though an increase in effi- tion loss. ciency is possible at higher temperatures. This is to test the per- Although we achieved a record for thermophotovoltaic cell efficiency (29.1%), a pathway to translate this into a complete formance of the proposed regenerative thermophotovoltaics within high-efficiency system would require further work on furnaces, the temperature ranges of practical furnaces. Our result is compared with results from Wernsman et al. (42), combustion product circulation, thermal management, geometrical where they used similar emitter temperature ranges, with a view factor, etc. The rear mirror reflectivity is a key determinant of corresponding photovoltaic cell bandgap of 0.63 eV. We get a thermophotovoltaic cell efficiency. Since the absorbed power is similar efficiency as Bechtel at 1,039 °C (peak efficiency in proportional to (1 − R), where R is close to 1, the subbandgap Bechtel’s experiment), even though our cells are not optimized reflectivity, R, of the cell needs to be measured very accurately. for operation at that temperature. Moreover, we achieve 29.1% We used bare evaporated as our reference for calibrating all efficiency at 1,207 °C, at a much lower temperature (2,027 °C) other reflectivity measurements, using a Nicolet iS50 spectrom- than the one used by Swanson et al. (31) to obtain similar efficiency eter. The observed reflectivity of bare gold was very reproducible. with . This is due to 2 key improvements of our device The optical constants of bare gold (47, 48) are used to calibrate the compared with previous results: 1) The reflectivity of our mirror Au reflectivity to 98.0%, when averaged over ±36° from the normal, reached 94.6% versus 90% in prior work (42), and 2) we have a and over both polarizations. better match of material bandgap to the Planck spectrum, leading The spectrally averaged measured reflectivity of our InGaAs/Au to superior performance. The optimum bandgap for a particular devices is 94.6%, versus 94.4% calculated for an InGaAs/Au reflector [using known optical constants (47, 48)]. The standard deviation of the average reflectivity is 94.6 ± 0.2%, after aver- Graphite emitter aging 70 runs over the specified random measurement ± 2.76mm error, 1%, of the spectrometer. This results in a thermopho- 0.72mm tovoltaic efficiency error of ∼29.1 ± 0.4%, due to reflectivity 2.62mm Cu baffle uncertainty. Note that the reflectivity from the optical constants and the measured reflectivity agree with one another within our 3.2mm 1.4mm reflectivity measurement accuracy window. We also analyzed the contribution to uncertainty from temperature dependence of 3.2mm - PV cell - emissivity and the EQE measurement. The statistical error in the

+ reflectivity measurement was by far the dominant contribution to Cu cell mount error in the thermophotovoltaic efficiency. Full details of this error analysis can be found in SI Appendix. Cooling water Now we project further improvements in thermophotovoltaic efficiency, as key device and chamber parameters improve. The key device parameters are the internal luminescence efficiency η ,se- Fig. 4. In our experiment, a planar graphite emitter is Joule-heated by a int ries resistance Rs, and the rear mirror reflectivity Rrear = 94.6%. A large . Beneath the emitter, a copper baffle is used to limit η the area of the photovoltaic cell exposed to illumination. The photovoltaic poor int is linked to significant loss of open-circuit voltage in the cell is mounted on a copper base, with water at 20 °C flowing through the photovoltaic cell (27). From our current−voltage curves, we extract copper mount. a series resistance Rs = 0.43 Ω and estimate ηint ≈ 82%,

Omair et al. PNAS | July 30, 2019 | vol. 116 | no. 31 | 15359 AB 1400 35 29.1% )

2 1200 30 1000 25 ( 800 20 y t i s

n 600 15 e d

r

e 400 10 w o

P200 mW/cm 5 TPV conversion efficiency (%) efficiency conversion TPV 0 0 600 700 800 900 1000 1100 1200 1300 600 700 800 900 1000 1100 1200 1300 Emitter temperature (oC) Emitter temperature (oC)

Fig. 6. (A) Black body power absorbed (blue) and electrical power (red) extracted by the photovoltaic cell. (B) Thermophotovoltaic (TPV) efficiency at dif- ferent emitter temperatures. The maximum efficiency is 29.1% at an emitter temperature of 1,207 °C. Results from our experiment are compared with similar results reported by Bechtel Bettis Inc. (42). Our results present the maximum thermophotovoltaic efficiency reported in the literature.

corresponding to ηext ≈ 3.5%. Based on these values of ηint, Rrear, the thermophotovoltaic efficiency to ∼48%, as shown by the R and s, we project the thermophotovoltaic efficiency of our cell at orange curve in Fig. 7. different temperatures (blue line in Fig. 7) and also compare it Further efficiency gains can be achieved using an antireflection with the experimentally measured values (dots). The efficiency coating, and by maximizing the emitter emissivity using silicon carbide > begins to diminish at emitter temperatures of 1,350 °C. Series as the thermal radiation source instead of graphite, since the former resistance limits the performance of the device in that temperature has an emissivity « = 0.96 versus « = 0.90 of the latter. This full set of range, where the brighter illumination gives rise to a larger short- improvements can to >50% power conversion efficiency in circuit current, and therefore larger resistive voltage drop. The an InGaAs thermophotovoltaic system, as shown by the black detailed procedure for estimating ηint and Rs from the current− voltage data is given in the SI Appendix. line in Fig. 7. Our setup differs from a thermophotovoltaic system in a full Although we have achieved a record for thermophotovoltaic chamber (as shown in Fig. 1A) in 2 key factors: 1) the geometric cell efficiency (29.1%), to translate this into a full thermophoto- view factor, which should be unity in the full chamber, and 2) the voltaic system would require further work on furnaces, combustion internal series resistance, which should be limited by the inherent product circulation, thermal management, and other elements. series resistance of the device. The latter can be approached via improved interconnect metallization in commercial devices. High series resistance penalizes the cell’s fill factor due to a resistive voltage drop. In our case, the device had an inherent 60 internal Rs ≈ 0.1 Ω, but we had an excess 0.33 Ω introduced by the wire bonds. If these technical difficulties are resolved, we project that such a system, using a photovoltaic cell identical to 50 ours, would have a power conversion efficiency of 33.6% at 1,207 °C. This projection is shown by the red line in Fig. 7. 40 The projected effect of improved subbandgap reflectivity, from an average value of 94.6 to 98%, is shown by the green curve in Fig. 7. This improvement in reflectivity can be obtained 30 by adding a layer of low dielectric between the rear gold layer and the semiconductor (49). 20 Improving the material quality of the photovoltaic device, R = 94.6%, R = 0.43Ω which we parameterize with the internal luminescence efficiency s ηint, leads to an enhancement in both operating and open-circuit 10 ηint = 82%, Feff= 0.31 . The internal luminescence efficiency of InGaAs is mainly affected by defect-mediated Shockley−Read−Hall recombination (%) conversion efficiency TPV 0 and, to a lesser extent, by intrinsic Auger recombination. The best 600 800 1000 1200 1400 1600 1800 2000 reported (50) values for InGaAs films reached τSRH ≈ 47 μs, with a − − o corresponding Auger coefficient ∼8.1 × 10 29 cm6·s 1.Forour Emitter temperature ( C) − − projection, we use a more moderate Shockley Read Hall lifetime Fig. 7. Projection of thermophotovoltaic (TPV) efficiency. Effects of device τSRH ≈ 10 μs, ∼2 orders of magnitude longer than the lifetime τ ≈ η and material quality, emitter, and chamber geometry on the system effi- SRH 60 ns in our device. This would increase the value of int ciency are illustrated. With the realistic projection of improvement in these to 98%. This improvement in the internal luminescence effi- key device and chamber parameters, more than 50% thermophotovoltaic ciency leads to a larger voltage in the photovoltaic cell, raising conversion efficiency is possible.

15360 | www.pnas.org/cgi/doi/10.1073/pnas.1903001116 Omair et al. Conclusion ACKNOWLEDGMENTS. The authors would like to thank Matin Amani and ± Kevin Cook for help with characterization. Experimental , measure- We have achieved 29.1 0.4% thermophotovoltaic power ment and data analysis were supported by Department of Energy (DOE) conversion efficiency, by reuse of unabsorbed subbandgap “Light-Material Interactions in Energy Conversion” Energy Frontier Research photons. We provide a roadmap to achieve higher efficiencies Center under Grant DE-SC0001293, DOE “ at Thermodynamic Limit” Energy Frontier Research Center under Grant DE-SC00019140, and by separately considering the realistic improvements of mate- Kavli Energy NanoScience Institute Heising-Simons Junior Fellowship of the rial, device, and chamber parameters. With the improvement of University of California, Berkeley. Setup design was supported in part by > Keck Foundation National Academies Keck Futures Initiative Grant. Device these parameters, it is possible to achieve 50% power con- fabrication was supported in part by the Alliance for , version efficiency using InGaAs photovoltaic cells. A highly LLC, the manager and operator of the National Labora- efficient thermophotovoltaic heat engine would be an excellent tory for the US DOE under Contract No. DE-AC36-08GO28308, funding pro- vided by the US DOE Office of Energy Efficiency and Renewable Energy Solar choice for hybrid automobiles, unmanned vehicles, and deep Energy Office. The views expressed in the article do not nec- space probes. essarily represent the views of DOE or the US Government.

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Omair et al. PNAS | July 30, 2019 | vol. 116 | no. 31 | 15361